a) Using trigonometry, we can set up a ratio to solve for the distance between the base of the ladder and the tree:
tan(70°) = opposite/adjacent
tan(70°) = x/7
x = 7 * tan(70°)
x ≈ 20.33
Therefore, the distance of the base of the ladder from the tree is approximately 20.33 meters.
b) The angle of depression is the angle between the imaginary line connecting Kevin's eyes to the basket and the horizontal ground. We can use trigonometry again to solve for this angle:
tan(θ) = opposite/adjacent
tan(θ) = 5.4/20.33
θ ≈ 15.7°
Therefore, the angle of depression is approximately 15.7 degrees.
Kevin is standing at the top of a ladder. The ladder is 7 m long. It is propped against a tree, and makes an
angle of 70° with the ground. To check his aim, Kevin is tossing balls into a basket located 5.4 m from the
base of the ladder, on the opposite side of the tree.
a) Determine the distance of the base of the ladder from the tree, in metres.
b) If Kevin’s eyes are even with the top of the ladder and he looks down on the basket, what is the angle of
depression? Answer to the nearest degree.
1 answer
1 answer